In the image, you are working with a linear regression model where the goal is to minimize the sum of squared errors (or residuals). You've already derived part of the equation to find the coefficients $a$ and $b$.

Let's continue from where the derivation left off:

The objective is to minimize the sum of squared errors:

$E = \sum (y_i - a - b x_i)^2$

Now, you are applying the condition that the derivative with respect to $a$ and $b$ equals zero to find the minimum:

1. First Derivative with respect to $a$: $\frac{\partial E}{\partial a} = \sum 2(y_i - a - b x_i)(-1) = 0$

Simplifying: $\sum (y_i - a - b x_i) = 0$

This gives you the first equation: $\sum y_i = n a + b \sum x_i$

2. First Derivative with respect to $b$: $\frac{\partial E}{\partial b} = \sum 2(y_i - a - b x_i)(-x_i) = 0$

Simplifying: $\sum x_i(y_i - a - b x_i) = 0$

This gives you the second equation: $\sum x_i y_i = a \sum x_i + b \sum x_i^2$

Now you have two normal equations:

1. $\sum y_i = n a + b \sum x_i$
2. $\sum x_i y_i = a \sum x_i + b \sum x_i^2$

Solving this system of equations will give you the coefficients $a$ and $b$.

Would you like me to continue solving this system, or would you like further clarification on any part of the process?